The joke is a metaphor.
In that scene, the Batman has asked the Joker how can he help him, maybe together they can find a way to really cure the Joker; this reminds him a joke, that goes along this line:
See, there were these two guys in a lunatic asylum... And one night,
one night they decide they don't like living in an asylum any more.
They decide ...
What was the conclusion of that scene or what was the actual meaning of that? I couldn't understand the ending of the movie.
It's intentionally left up the audience to figure out what it means. It is lifted straight out of the source material, the 1988 "The Killing Joke" by Alan Moore and Brian Bolland. So much so that 20 years later, Bolland explains the ...
The assault is specifically to torment Jim Gordon, not a random act of violence (as far as all of the Joker's actions are random acts of violence), but it's just done to prove his point.
Spoilered due to content:
The plot revolves around the Joker's plan to make a point, that any normal person could go insane after just one bad day. He targets Commissioner ...
They just laugh together
Since relevant, I'll refer to the comic, on which the movie's based.
Both other answers are on track.
Context for several views on this story
It's commonly regarded, as by cde, to be an open end: it's claimed to be what the script shows.
There's even material to say, as by mattiav27, that Batman kills the Joker, and this is what ...